The obtained \(H_{c2}\) (0), combined with other superconducting parameters such as the lower critical field \(H_{c1}\) , London penetration depth \(\lambda _L\) , and coherence length \(\xi \) , are crucial to the understanding of the physical properties and the mechanism of superconductivity of a type-II superconductor. The \(H_{c1}\)  is determined by the magnetic-field dependence of the \(dc\)  magnetization \(M(H)\)  at various temperatures below \(T_c\)  [Fig. 3(c)]. Within this method, the magnetic field that initially deviates from the linear \(M(H)\)  behaviour is defined as \(H_{c1}(T)\)  for a given temperature, as illustrated in the upper right of Fig. 3(d). The \(H_{c1}(T)\)  values at different temperatures plotted in Fig. 3(d) are used to determine \(H_{c1}\) (0) of 6.9\(\pm \) 0.1 mT through the empirical relation [1]} \(H_{c1}(T)/H_{c1}(0)=1-(T/T_c)^2\) . With these critical fields, \(\lambda _L\)  and the Ginzburg-Landau coherence length (\(\xi _{GL}\) ) can be determined by using the equations: \(H_{c2}(0)=\Phi _0/2\pi \xi _{GL}^2\)  and \(H_{c1}(0)=(\Phi _0/4\pi \lambda _L^2)\ln (\lambda _L/\xi _{GL})\)  with the flux quantum \(\Phi _{0}=2.0678\times 10^{-15}\)  Wb. We thus have \(\lambda _L\) =3325\(\pm \) 36 Å, \(\xi _{GL}\) =31.6\(\pm \) 0.3 Å, and the Ginzburg-Landau parameter \(\kappa =\lambda _L/\xi _{GL}=105\pm 2\) . These results are compared with those determined by using various techniques such as the magnetization [2]}, [3]}, [4]}, [5]}, magnetoresistance [6]}, muon spin relaxation [7]}, [8]}, nuclear magnetic resonance [9]}, [10]}, and optical reflectivity [11]}.
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